A two-species weak competition system of reaction-diffusion-advection with double free boundaries

Bo Duan; Zhengce Zhang

doi:10.3934/dcdsb.2018208

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2019, Volume 24, Issue 2: 801-829. Doi: 10.3934/dcdsb.2018208

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A two-species weak competition system of reaction-diffusion-advection with double free boundaries

Bo Duan and
Zhengce Zhang^,

School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China

* Corresponding author
* Corresponding author

Received: July 31, 2017

Revised: November 30, 2017

Early access: June 2018

Published: January 2019

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Abstract

In this paper, we investigate a two-species weak competition system of reaction-diffusion-advection with double free boundaries that represent the expanding front in a one-dimensional habitat, where a combination of random movement and advection is adopted by two competing species. The main goal is to understand the effect of small advection environment and dynamics of the two species through double free boundaries. We provide a spreading-vanishing dichotomy, which means that both of the two species either spread to the entire space successfully and survive in the new environment as time goes to infinity, or vanish and become extinct in the long run. Furthermore, if the spreading or vanishing of the two species occurs, some sufficient conditions via the initial data are established. When spreading of the two species happens, the long time behavior of solutions and estimates of spreading speed of both free boundaries are obtained.

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Mathematics Subject Classification: Primary: 35R35; Secondary: 35K60.

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